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44001

44001²± 2 are primes.

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44016

44016² = 1937408256, a square with different digits.

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

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44032

44032² = (1² + 7)(5² + 7)(6² + 7)(11² + 7)(37² + 7) = (6² + 7)(37² + 7)(181² + 7).

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44047

44047² = 1536² + 1537² + 1538² + 1539² + ... + 2113².

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

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44048

1² + 2² + 3² + 4² + ... + 44048² = 28488666200024, which consists of even digits.

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

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44049

44049²± 2 are primes.

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44064

435² + 44064 = 483², 435² - 44064 = 381².

44064² = (1² + 8)(2² + 8)(3² + 8)(4² + 8)(10² + 8)(20² + 8)
= (1² + 8)(2² + 8)(8² + 8)(10² + 8)(48² + 8) = (1² + 8)(4² + 8)(10² + 8)(14² + 8)(20² + 8)
= (2² + 8)(3² + 8)(4² + 8)(14² + 8)(44² + 8) = (2² + 8)(14² + 8)(20² + 8)(44² + 8).

Page of Squares : First Upload August 4, 2012 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44065

44065² = (13² + 6)(3331² + 6).

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44070

44070² = (2² + 9)(45² + 9)(271² + 9).

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44079

The quadratic polynomial -44079X² + 416346X - 173351 takes the values 446², 695², 824², 887², 898², 859² at X = 1, 2,..., 6

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

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44110

44110²± 3 are primes.

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44118

44118² = 3191 x 3192 + 3193 x 3194 + 3195 x 3196 + 3197 x 3198 + ... + 3533 x 3534.

44118² = (1² + 2)(6² + 2)(59² + 2)(70² + 2).

Page of Squares : First Upload August 4, 2012 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44127

1² + 2² + 3² + 4² + ... + 44127² = 28642222628880, which consists of even digits.

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

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44138

44138² = (1² + 1)(39² + 1)(800² + 1).

Page of Squares : First Upload November 9, 2013 ; Last Revised November 9, 2013
by Yoshio Mimura, Kobe, Japan

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44200

44200² = (1² + 1)(3² + 1)(5² + 1)(7² + 1)(13² + 1)(21² + 1)
= (1² + 4)(2² + 4)(9² + 4)(26² + 4)(29² + 4) = (1² + 4)(3² + 4)(4² + 4)(8² + 4)(9² + 4)(16² + 4)
= (1² + 4)(3² + 4)(4² + 4)(16² + 4)(76² + 4) = (1² + 1)(3² + 1)(5² + 1)(7² + 1)(13² + 1)(21² + 1)
= (1² + 4)(3² + 4)(6² + 4)(9² + 4)(94² + 4) = (1² + 4)(3² + 4)(9² + 4)(14² + 4)(42² + 4)
= (1² + 4)(4² + 4)(8² + 4)(536² + 4) = (2² + 4)(3² + 4)(9² + 4)(11² + 4)(42² + 4)
= (3² + 4)(4² + 4)(8² + 4)(9² + 4)(36² + 4) = (3² + 4)(4² + 4)(36² + 4)(76² + 4)
= (3² + 4)(9² + 4)(14² + 4)(94² + 4) = (3² + 4)(11² + 4)(26² + 4)(42² + 4)
= (6² + 4)(9² + 4)(26² + 4)(29² + 4) = (8² + 4)(9² + 4)(16² + 4)(36² + 4)
= (9² + 4)(10² + 4)(11² + 4)(42² + 4) = (9² + 4)(42² + 4)(114² + 4)
= (11² + 4)(42² + 4)(94² + 4) = (16² + 4)(36² + 4)(76² + 4).

Page of Squares : First Upload November 9, 2013 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44244

44244² = 1957531536, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013
by Yoshio Mimura, Kobe, Japan

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44254

44254²± 3 are primes.

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44275

44275² = 1960275625, and 196 = 14², 275625 = 525².

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

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44319

44319²± 2 are primes.

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44352

44352² = (7² - 1)(10² - 1)(15² - 1)(43² - 1) = (10² - 1)(13² - 1)(15² - 1)(23² - 1).

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44367

44367²± 2 are primes.

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44370

44370² = (1² + 9)(6² + 9)(7² + 9)(12² + 9)(22² + 9) = (1² + 9)(12² + 9)(22² + 9)(51² + 9)
= (1² + 9)(114² + 9)(123² + 9) = (3² + 9)(4² + 9)(7² + 9)(12² + 9)(22² + 9)
= (3² + 9)(6² + 9)(1559² + 9) = (3² + 9)(22² + 9)(471² + 9) = (4² + 9)(5² + 9)(12² + 9)(123² + 9)
= (5² + 9)(6² + 9)(22² + 9)(51² + 9) = (5² + 9)(9² + 9)(22² + 9)(36² + 9)
= (6² + 9)(7² + 9)(22² + 9)(39² + 9) = (7² + 9)(12² + 9)(21² + 9)(22² + 9)
= (7² + 9)(12² + 9)(471² + 9) = (7² + 9)(51² + 9)(114² + 9) = (12² + 9)(29² + 9)(123² + 9)
= (22² + 9)(39² + 9)(51² + 9).

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44376

215² + 44376 = 301², 215² - 44376 = 43².

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

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44457

44457²± 2 are primes.

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44460

44460² = (2² - 1)(4² - 1)(39² - 1)(170² - 1) 44460,(2² - 1)(151² - 1)(170² - 1).

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44522

44522² = (14² + 1)(15² + 1)(211² + 1).

Page of Squares : First Upload November 9, 2013 ; Last Revised November 9, 2013
by Yoshio Mimura, Kobe, Japan

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44523

44523² = (1² + 2)(7² + 2)(17² + 2)(211² + 2).

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44528

44528² = (2² + 7)(4² + 7)(13² + 7)(211² + 7).

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44590

44590² = 995² + 997² + 999² + 1001² + ... + 2345².

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

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44623

44623² = 1991212129, a square with 3 kinds of digits.

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

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44632

44632² = 716 x 717 + 718 x 719 + 720 x 721 + 722 x 723 + 724 x 725+ ... + 2308 x 2309.

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

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44642

44642² = (1² + 1)(10² + 1)(3141² + 1)
= (1² + 1)(5² + 1)(10² + 1)(616² + 1) = (4² + 1)(21² + 1)(515² + 1).

Page of Squares : First Upload November 9, 2013 ; Last Revised November 9, 2013
by Yoshio Mimura, Kobe, Japan

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44654

44654² = 1993979716, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013
by Yoshio Mimura, Kobe, Japan

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4655

44657²± 2 are primes.

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44660

44660² = (1² + 6)(2² + 6)(4² + 6)(8² + 6)(136² + 6) = (2² + 6)(4² + 6)(22² + 6)(136² + 6).

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44678

44678²± 3 are primes.

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44688

44688² = (1² + 3)(2² + 3)(3² + 3)(4² + 3)(9² + 3)(61² + 3)
= (1² + 3)(2² + 3)(3² + 3)(4² + 3)(15² + 3)(37² + 3) = (1² + 3)(2² + 3)(9² + 3)(15² + 3)(61² + 3)
= (1² + 3)(3² + 3)(4² + 3)(5² + 3)(12² + 3)(23² + 3) = (1² + 3)(4² + 3)(9² + 3)(15² + 3)(37² + 3)
= (1² + 3)(5² + 3)(12² + 3)(15² + 3)(23² + 3) = (2² + 3)(3² + 3)(4² + 3)(5² + 3)(9² + 3)(23² + 3)
= (2² + 3)(3² + 3)(5² + 3)(15² + 3)(61² + 3) = (2² + 3)(5² + 3)(9² + 3)(15² + 3)(23² + 3)
= (3² + 3)(4² + 3)(5² + 3)(9² + 3)(61² + 3) = (3² + 3)(4² + 3)(5² + 3)(15² + 3)(37² + 3)
= (3² + 3)(9² + 3)(23² + 3)(61² + 3) = (3² + 3)(15² + 3)(23² + 3)(37² + 3)
= (5² + 3)(9² + 3)(15² + 3)(61² + 3).

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44704

44704² = (2² + 7)(45² + 7)(299² + 7).

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44734

(44734² +2) = (1² + 2)(3² + 2)(4² + 2)(7² + 2)(15² + 2)(17² + 2).

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

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44798

44798² = 2006860804, a square with even digits.

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

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44814

44814²± 5 are primes.

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44884

44884²± 3 are primes.

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44913

44913²± 2 are primes.

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44928

44928² = (2² - 1)(3² - 1)(7² - 1)(25² - 1)(53² - 1) = (5² - 1)(7² - 1)(25² - 1)(53² - 1).

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44936

44936²± 3 are primes.

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44946

44946² = (1² + 2)(2² + 2)(3² + 2)(15² + 2)(212² + 2) = (1² + 2)(8² + 2)(15² + 2)(212² + 2)
= (3² + 2)(4² + 2)(15² + 2)(212² + 2) = (14² + 2)(15² + 2)(212² + 2).

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44950

44950² = (2² + 6)(5² + 6)(38² + 6)(67² + 6) = (2² + 6)(67² + 6)(212² + 6)
= (5² + 6)(38² + 6)(212² + 6).

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44954

44954² = (2² + 3)(124² + 3)(137² + 3).

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44978

44978²± 3 are primes.

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44944

44944 = 212², a palindromic square with 2 kinds of digits.

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

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44988

44988²± 5 are primes.

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44990

44990²± 3 are primes.

Page of Squares : First Upload March 8, 2014 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

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44992

44992² = 2024280064, a square with even digits.

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

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44998

44998² = 2024820004, a square with even digits.

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

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